Rotating Shell Dynamics

Chapter 1. Introduction

1.1 Rotating Shells of Revolution

1.2 Historical Development of the Dynamics of Shells

1.3 About This Monograph


Chapter 2. Fundamental Theory of Rotating Shells of Revolution

2.1 Basic Considerations and Assumptions

2.2 Shell Kinematic Strain-Displacement Relations

2.3 Resultant Stress-Strain Relations in Constitutive Shell Models

2.4 Governing Equations of Motion

2.5 Eigenvalue Analysis of Boundary Value Problems


Chapter 3. Free Vibration of Thin Rotating Cylindrical Shells

3.1 Introduction

3.2 Theoretical Development: Rotating Thin Cylindrical Shell

3.3 Numerical Implementation

3.3.1 Galerkin’s Method (Characteristic Beam Functions)

3.3.2 Convergence Characteristics and Numerical Validation

3.4 Frequency Characteristics

3.4.1 Influence of Coriolis and Centrifugal Effects

3.4.2 Different Thin Shell Theories

3.4.3 Influence of Rotating Velocity

3.4.4 Influence of Length and Thickness

3.4.5 Influence of Layered Configuration of Composites

3.4.6 Influence of Boundary Condition

3.4.7 Discussion on Modal Wave Numbers
Appendix


Chapter 4. Free Vibration of Thin Rotating Conical Shells

4.1 Introduction

4.2 Theoretical Development: Rotating Conical Shell

4.3 Numerical Implementation

4.3.1 Assumed-Mode Method and Generalised Differential Quadrature

4.3.2 Convergence Characteristics and Numerical Validation

4.4 Frequency Characteristics

4.4.1 Influence of Rotating Velocity

4.4.2 Influence of Cone Angle

4.4.3 Influence of Length and Thickness

4.4.4 Influence of Orthotropy and Layered Configuration of Composites

4.4.5 Influence of Boundary Condition

4.4.6 Influence of Initial Stress

4.4.7 Discussion on Wave Number
Appendices


Chapter 5. Free Vibration of Thick Rotating Cylindrical Shells

5.1 Introduction

5.2 Natural Frequency Analysis by Mindlin Shell Theory

5.2.1 Rotating Mindlin Shell Theory - Development

5.2.2 Numerical Validation and Comparison

5.2.3 Frequency Characteristics

5.3 Analysis of Vibrational Mode by FEM with Nonlinear Kinematics

5.3.1 Classification of 3-D Modes of Thick Rotating Cylindrical Shells

5.3.2 Numerical Implementation

5.3.3 Influence of Rotation on Frequencies of Various 3-D Modes


Chapter 6. Critical Speed and Dynamic Stability of Thin Rotating Isotropic Cylindrical Shells

6.1 Introduction

6.2 Theoretical Development: Axially Loaded Rotating Shells

6.3 Numerical Implementation

6.3.1 Critical Speed Analysis

6.3.2 Dynamic Stability Analysis

6.4 Critical Speeds and Instability Regions

6.4.1 Influence of Axial Loading on Critical Speeds

6.4.2 Parametric Studies on Dynamic Stability


References

Author Index

Subject Index